Singular point: How can I numerically find the point of fracture?

Tell me please how can I numerically find the point of fracture, such as in this graph for example:
I would like to know what methods exist for solving this problem (also for the multidimensional case), and references to them.

If all you are given is the graph, the all you can do is estimate the value from the graph. It looks to me like it is about (98.75, -.98). If you have the graph in a graphing calculator, you may be able to "zoom" in on the point to get more accuracy.

No, I don't know. Each point on the graph is the result of solving systems of nonlinear equations, whose form depends on several parameters. Ordinate is one of the parameters, Abscissa - one of unknown variables.

If all you are given is the graph, the all you can do is estimate the value from the graph. It looks to me like it is about (98.75, -.98). If you have the graph in a graphing calculator, you may be able to "zoom" in on the point to get more accuracy.

It is possible if a man analizes the grath. But in my case computer must deturmine point of fracture without a man